Abstract:

Described are embodiments for slice-selective excitation for MRI that
utilize multiple RF transmit coils, each of which are driven with a
separate independent current waveform. These embodiments allow
slice-selective excitation with slice profile and excitation time similar
to other single-channel excitation, but with reduction in SAR caused by
the transverse component of the RF field by a factor up to the number of
excitation coils.

Claims:

1. A method, of reducing a specific absorption rate (SAR) over a field of
view of an imaged object during magnetic imaging (MRI),
comprising:emitting a first radiofrequency (RF) pulse into an object with
an RF excitation coil element that has a first sensitivity profile
comprising (a) a substantially uniform amplitude, and (b) a first phase
that is substantially constant in a direction across an imaging volume of
the object;emitting a second RF pulse into the object with a second RF
excitation coil element that has a second sensitivity profile comprising
(a) a substantially uniform amplitude, and (b) a second phase that varies
substantially linearly, with a first nonzero integer multiple of 2.pi.
phase variation, in the direction across the imaging volume; andemitting
a third RF pulse into the object with a third RF excitation coil element
that has a third sensitivity profile comprising (a) a substantially
uniform amplitude and (b) a third phase that varies substantially
linearly, with a second nonzero integer multiple of -2.pi. phase
variation, in the direction across the imaging volume;wherein an improved
SAR, resulting from emission of the first, second, and third RF pulses
over a field of view of the object, is decreased relative to an
unimproved SAR, resulting from emission of a fourth RF pulse that would
produce substantially the same amount of transverse magnetization as the
emission of the first, second, and third RF pulses over the field of
view.

2. The method of claim 1, wherein RF pulses are emitted into the object by
n RF coil elements.

3. The method of claim 2, wherein n≧3.

4. The method of claim 2, wherein the improved SAR is reduced by about a
factor of n relative to the unimproved SAR.

5. The method of claim 1, wherein the first and second nonzero integers
are positive integers.

6. The method of claim 1, wherein the first and second nonzero integers
are the same positive integer.

7. The method of claim 1, wherein the first phase is substantially zero
across the imaging volume.

8. The method of claim 1, wherein each of the first, second, and third RF
pulses comprises a waveform that is substantially identical in shape to,
but shifted in time relative to, each of the others of the first, second,
and third waveforms.

9. A method, of reducing a specific absorption rate (SAR) over a field of
view of an imaged object during magnetic imaging (MRI),
comprising:emitting a first radiofrequency (RF) pulse into an object with
an RF excitation coil element that has a first sensitivity profile
comprising a first phase that is substantially constant across an imaging
volume of the object;emitting a second RF pulse into the object with a
second RF excitation coil element that has a second sensitivity profile
comprising a second phase that varies substantially linearly, with a
first nonzero integer multiple of 2.pi. phase variation, in a direction
across the imaging volume; andemitting a third RF pulse into the object
with a third RF excitation coil element that has a third sensitivity
profile comprising a third phase that varies substantially linearly, with
a second nonzero integer multiple of -27l π phase variation, in the
direction across the imaging volume;wherein an improved SAR, resulting
from emission of the first, second, and third RF pulses over a field of
view of the object, is decreased relative to an unimproved SAR, resulting
from emission of a fourth RF pulse that would produce substantially the
same amount of transverse magnetization as the emission of the first,
second, and third RF pulses over the field of view.

10. The method of claim 9, wherein RF pulses are emitted into the object
by n RF coil elements.

14. The method of claim 9, wherein the improved SAR varies spatially
across the field of view.

15. The method of claim 10, wherein the improved SAR is reduced by about a
factor of n relative to the unimproved SAR.

16. The method of claim 9, wherein the first and second nonzero integers
are positive integers.

17. The method of claim 9, wherein the first and second nonzero integers
are the same positive integer.

18. The method of claim 9, wherein the first phase is substantially zero
across the imaging volume.

19. The method of claim 9, wherein each of the first, second, and third RF
pulses comprises a waveform that is substantially identical in shape to,
but shifted in time relative to, each of the others of the first, second,
and third waveforms.

20. A system, for reducing a specific absorption rate (SAR) over a field
of view of an imaged object during magnetic imaging (MRI), comprising:a
transmit module, programmed to:emit a first radiofrequency (RF) pulse
into an object with an RF excitation coil element that has a first
sensitivity profile comprising a first phase that is substantially
constant across an imaging volume of the object;emit a second RF pulse
into the object with a second RF excitation coil element that has a
second sensitivity profile comprising a second phase that varies
substantially linearly, with a first nonzero integer multiple of 2.pi.
phase variation, in a direction across the imaging volume; andemit a
third RF pulse into the object with a third RF excitation coil element
that has a third sensitivity profile comprising a third phase that varies
substantially linearly, with a second nonzero integer multiple of -2.pi.
phase variation, in the direction across the imaging volume;wherein an
improved SAR, resulting from emission of the first, second, and third RF
pulses over a field of view of the object, is decreased relative to an
unimproved SAR, resulting from emission of a fourth RF pulse that would
produce substantially the same amount of transverse magnetization as the
emission of the first, second, and third RF pulses over the field of
view.

[0004]Magnetic resonance imaging (MRI) is a common modality for imaging
joints and other parts of the body due to its excellent definition of
ligaments, cartilage, bone, muscle, fat and superior soft tissue
contrast. Many MR techniques have been able to provide information about
late stages of degeneration in which structural defects are present.

[0005]When a substance, such as human tissue, is subjected to a uniform
magnetic field, the individual magnetic moments of the spins in the
tissue attempt to align with this polarizing field, but precess about it
in random order at their characteristic Larmor frequency. If the
substance, or tissue, is subjected to a magnetic field that is in the x-y
plane, and which is near the Larmor frequency, the net aligned moment, or
"longitudinal magnetization," may be rotated, or "tipped," into the x-y
plane to produce a net transverse magnetic moment. A signal is emitted by
the excited spins after the excitation signal is terminated, and this
signal may be received and processed to form an image.

[0006]When utilizing these signals to produce images, magnetic field
gradients are employed. Often, the region to be imaged is scanned by a
sequence of measurement cycles in which these gradients vary according to
the particular localization method being used. The resulting set of
received nuclear magnetic resonance (NMR) signals are digitized and
processed to reconstruct the image using a reconstruction technique.

SUMMARY OF THE INVENTIONS

[0007]Disclosed are embodiments of slice selective excitation that utilize
multiple RF transmit coils. In some embodiments, each coil is driven by a
separate independent control channel, which achieves slice selection with
markedly decreased specific absorption rate (SAR), which is a measure of
patient heating. Reduced SAR is achieved, in embodiments described
herein, with little or no change in slice profile and little or no
significant increase in excitation time.

[0008]In some embodiments, methods and apparatus are described for
reducing a specific absorption rate (SAR) over a field of view of an
imaged object during magnetic imaging (MRI). Some embodiments include the
steps of emitting a first radiofrequency (RF) pulse into an object with
an RF excitation coil element that has a first sensitivity profile
comprising (a) a substantially uniform amplitude, and (b) a first phase
that is substantially constant in a direction across an imaging volume of
the object; emitting a second RF pulse into the object with a second RF
excitation coil element that has a second sensitivity profile comprising
(a) a substantially uniform amplitude, and (b) a second phase that varies
substantially linearly, with a first nonzero integer multiple of 2π
phase variation, in the direction across the imaging volume; and emitting
a third RF pulse into the object with a third RF excitation coil element
that has a third sensitivity profile comprising (a) a substantially
uniform amplitude and (b) a third phase that varies substantially
linearly, with a second nonzero integer multiple of -2π phase
variation, in the direction across the imaging volume.

[0009]In some embodiments, an improved SAR, resulting from emission of the
first, second, and third RF pulses over a field of view of the object, is
decreased relative to an unimproved SAR, resulting from emission of a
fourth RF pulse that would produce substantially the same amount of
transverse magnetization as emission of the first, second, and third RF
pulses over the field of view.

[0010]Some embodiments provide that RF pulses are emitted into the object
by n RF coil elements, and in certain embodiments, n≧3. In some
embodiments, the improved SAR is reduced by about a factor of n relative
to the unimproved SAR. In some embodiments, the first and second nonzero
integers are positive integers. Some embodiments provide that the first
and second nonzero integers are the same positive integer. In certain
embodiments, the first phase is substantially zero across the imaging
volume. In some embodiments, each of the first, second, and third RF
pulses comprises a waveform that is substantially identical in shape to,
but shifted in time relative to, each of the others of the first, second,
and third waveforms.

[0011]Some embodiments provide methods for reducing a specific absorption
rate (SAR) over a field of view of an imaged object during magnetic
imaging (MRI) that include emitting a first radiofrequency (RF) pulse
into an object with an RF excitation coil element that has a first
sensitivity profile comprising a first phase that is substantially
constant across an imaging volume of the object; emitting a second RF
pulse into the object with a second RF excitation coil element that has a
second sensitivity profile comprising a second phase that varies
substantially linearly, with a first nonzero integer multiple of 2π
phase variation, in a direction across the imaging volume; and emitting a
third RF pulse into the object with a third RF excitation coil element
that has a third sensitivity profile comprising a third phase that varies
substantially linearly, with a second nonzero integer multiple of -2π
phase variation, in the direction across the imaging volume.

[0012]In some embodiments, an improved SAR, resulting from emission of the
first, second, and third RF pulses over a field of view of the object, is
decreased relative to an unimproved SAR, resulting from emission of a
fourth RF pulse that would produce substantially the same amount of
transverse magnetization as emission of the first, second, and third RF
pulses over the field of view.

[0013]In some embodiments, RF pulses are emitted into the object by n RF
coil elements, and in certain embodiments, n≧3. In some
embodiments, RF pulses are transmitted via n RF channels, and in certain
embodiments, n≧3. Some embodiments provide that the improved SAR
varies spatially across the field of view. In some embodiments, the
improved SAR is reduced by about a factor of n relative to the unimproved
SAR.

[0014]Some embodiments provide that the first and second nonzero integers
are positive integers. In some embodiments, the first and second nonzero
integers are the same positive integer. In certain embodiments, the first
phase is substantially zero across the imaging volume. Some embodiments,
provide that each of the first, second, and third RF pulses comprises a
waveform that is substantially identical in shape to, but shifted in time
relative to, each of the others of the first, second, and third
waveforms.

[0015]Some embodiments described herein relate to a system, for reducing a
specific absorption rate (SAR) over a field of view of an imaged object
during magnetic imaging (MRI), that includes a transmit module. In some
embodiments, the transmit module is programmed to emit a first
radiofrequency (RF) pulse into an object with an RF excitation coil
element that has a first sensitivity profile comprising a first phase
that is substantially constant across an imaging volume of the object;
emit a second RF pulse into the object with a second RF excitation coil
element that has a second sensitivity profile comprising a second phase
that varies substantially linearly, with a first nonzero integer multiple
of 2π phase variation, in a direction across the imaging volume; and
emit a third RF pulse into the object with a third RF excitation coil
element that has a third sensitivity profile comprising a third phase
that varies substantially linearly, with a second nonzero integer
multiple of -2π phase variation, in the direction across the imaging
volume. In some embodiments, an improved SAR, resulting from emission of
the first, second, and third RF pulses over a field of view of the
object, is decreased relative to an unimproved SAR, resulting from
emission of a fourth RF pulse that would produce substantially the same
amount of transverse magnetization as emission of the first, second, and
third RF pulses over the field of view.

[0016]For purposes of summarizing the disclosure, certain aspects,
advantages, and novel features of the disclosure have been described
herein. It is to be understood that not necessarily all such advantages
may be achieved in accordance with any particular embodiment of the
disclosure. Thus, the disclosure may be embodied or carried out in a
manner that achieves or optimizes one advantage or group of advantages as
taught herein without necessarily achieving other advantages as may be
taught or suggested herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]General descriptions provided herein that implement various features
of the disclosure will now be described with reference to the drawings.
The drawings and the associated descriptions are provided to illustrate
embodiments of the disclosure and not to limit the scope of the
disclosure.

[0018]FIG. 1A depicts a RF envelope and z gradient current waveforms of a
slice-selective excitation.

[0041]FIG. 12 depicts a schematic representation of an MRI transmit module
in accordance with embodiments described herein.

DETAILED DESCRIPTION OF THE INVENTIONS

[0042]Described herein are embodiments for slice-selective excitation for
MRI that utilize multiple RF transmit coils, each of the coils being
driven with a separate independent current waveform. These embodiments
allow slice-selective excitation with slice profile and excitation time
similar to conventional single-channel excitation but with reduction in
SAR caused by the transverse component of the RF field by a factor up to
the number of excitation coils.

[0043]Results described herein are based on numerical integration of the
Bloch equation, neglecting T1 and T2 relaxation. Transverse SAR was
calculated by summing over time the square amplitude of the transverse
component of the RF field B1 at each spatial location, which depends on
the individual RF waveforms and coil sensitivity profiles.

Conventional Slice-Selective Excitation

[0044]Slice-selective excitation is achieved by applying a current to the
RF excitation coil which is modulated at the proton resonant frequency
(64 MHz for a 1.5 Tesla main field strength), with a time envelope which
is approximately equal to the Fourier transform of the desired slice
profile. A constant gradient field is applied during the excitation
process. The direction of the gradient determines the orientation of the
selected slice, and the gradient strength determines the thickness of the
slice profile. Excitation is typically performed with a coil designed for
optimal field uniformity.

[0045]FIGS. 1A-1C depict a conventional slice-selective excitation. FIG.
1A depicts RF envelope and z gradient current waveforms. The RF envelope
was designed by Fourier transform with Hamming window. FIG. 1B depicts a
slice profile in z, assuming uniform RF coil sensitivity. Units are
fraction of maximum possible transverse magnetization MZO. FIG. 1C
depicts the SAR resulting from the transverse component of B1. For
conventional slice selection, the SAR is constant across the field of
view, whether in or out of slice.

[0046]With a substantially uniform RF field, the SAR of a conventional
slice-selective pulse is the same over the entire sensitive volume of the
coil. Areas both within and without the selected slice experience the
same RF field strength over time, and hence the same SAR, but the time
sequence of tips adds to zero in areas outside the selected slice and
adds to the desired flip angle in areas within the slice.

[0047]FIGS. 1A-1C illustrates conventional slice-selective excitation.
FIG. 1A shows an RF time envelope and gradient current waveform. The RF
waveform was designed by Fourier transform and has the form of a sine
function multiplied by a Hamming window function. The waveform is scaled
for a 90° flip angle. FIG. 1B shows the resulting transverse
magnetization in its components Mx and My achieved by this excitation if
performed with an RF coil having uniform amplitude and constant phase
sensitivity profile. Units are in fraction of the equilibrium
longitudinal magnetization MZO. The non-zero value of Mx within the
slice profile is a consequence of violation of the low-flip angle
assumption upon which RF design by Fourier transform is based, and is
generic to any RF pulse designed by the Fourier transform method. FIG. 1C
shows the SAR due to the component of B1 in the transverse x-y plane. SAR
due to B1 in the z axis is not considered. Units of SAR in FIG. 1C are
arbitrary.

Slice-Selective Excitation with Multiple Coils

[0048]When multiple RF coils are used, a pattern of destructive and
constructive interference of the RF fields from each coil can result in
decreased SAR in some regions of the imaging volume. With appropriately
designed RF coils, RF coil current waveforms, and gradient waveforms,
slice selective excitation can be achieved with greatly reduced SAR. As
used herein, the term "coil element" is a broad term and can refer to an
RF coil or a component of an RF coil that sends an RF signal via an RF
channel. In some embodiments, an RF coil may comprise multiple RF coil
elements.

[0049]SAR reduction is obtained by a factor of 3 for a system of three
independent RF current sources and three different RF coils. The
underlying principle may be extended to any number of coils and RF
channels, with SAR reduction factor up to the number of coils and
channels.

[0050]FIG. 2 depicts a coil sensitivity profile phase for a 3-coil
embodiment. Coil 1 has a constant sensitivity amplitude and a zero phase.
Coil 2 has a constant amplitude but a phase which varies linearly in z.
Coil 3 has a constant amplitude but a phase which varies inversely
linearly in z. Coil amplitude and phase refer to amplitude and phase in
the x-y plane, neglecting the RF field in the z direction (B1z), which
does not contribute to excitation. B1z does contribute to SAR, and
minimization of B1z can be a goal of coil design.

[0051]In some embodiments, a set of RF coils that can be designated as a
"linear phase" coil configuration. In this configuration, one coil has a
sensitivity profile with a uniform amplitude and a constant phase across
the imaging volume. The second coil has a uniform amplitude but a phase
that varies linearly in a single direction with a total of 2π phase
variation across the imaging volume. The third coil has a uniform
amplitude but a phase that varies linearly in the same direction with a
total variation of -2π radians. The phase of the coil sensitivity
profile for these three coils is illustrated in FIG. 2. For concreteness,
the direction of phase variation can be considered to be the z axis, the
direction of the main field. Phase variation in any direction could be
used with the proposed method of slice selection. The z axis can be
selected, in some embodiments, for concrete illustration because coil
designs exist which give the desired coil sensitivity with nearly uniform
amplitude and with linear phase distribution along the z axis. One
physical realization of such an RF coil set would be a set of three
birdcage coils which are arranged coaxially along the z axis, with the
second coil twisted to give +2π radians phase variation across the z
field of view, and the third coil twisted to give -2π radians phase
variation across the z field of view. A twisted birdcage coil having such
a linear phase property has been described in Alsop D C, Connick T J,
Mizsei G., A spiral volume coil for improved RF field homogeneity at high
static magnetic field strength, Magn Reson Med 1998; 40(1):49-54, the
entirety of which is incorporated herein and made a part of this
specification. An alternative physical realization would consist of
coaxial birdcage coils with an external shield separated from the
birdcage rungs by a dielectric, as described in Foo T K, Hayes C E, Kang
Y W, Reduction of RF penetration effects in high field imaging, Magn
Reson Med 1992; 23(2):287-301, the entirety of which is incorporated
herein and made a part of this specification.

[0052]In this context, the phase and amplitude referred to are of the
component of the coil sensitivity profile which lies in the transverse
x-y plane of the MRI system, i.e. the plane perpendicular to the main
field. The z component of the RF coil sensitivity profile is neglected.
The z component of the RF field does not contribute to excitation, but is
a source of SAR. Coil design optimization can be performed to minimize
the z component of the RF field. Reduction in SAR with the current method
refers only to the component of SAR related to the RF field in the
transverse x-y plane.

[0053]The RF waveforms for all three coils are calculated independently as
if the coils were to be used singly to achieve a conventional slice
selective excitation. One example of a suitable RF waveform design
process would be the Fourier transform method. The RF waveform for the
second coil (with +2π linear phase) is designed by replicating the RF
waveform of coil 1, but shifting it in time. The time shift length is
chosen so that the amount of linear phase which accumulates during the
interval due to the gradient field is equal to the linear phase of the RF
coil. Specifically, if a given coil has linear phase of 2 nπ across
the FOV, the time shift Δt of the RF waveform for this coil
relative to the RF waveform of the coil with constant phase (designated
coil 1 in our concrete 3-coil scenario) is

Δt=2nπ/γG (1.1)

where G is the gradient strength of the slice-select gradient (Gz in our
implementation) and γ is the gyromagnetic ratio in units of radians
per unit gradient strength.

[0054]Similarly, the RF waveform for the third coil is shifted by a
corresponding time increment which, for this particular coil
configuration, will be the negative of the time shift of the second
coil's waveform. Finally, the amplitude of each RF waveform is multiplied
by a factor of 1/3. The resulting RF current waveforms for each of the
three channels are shown in FIG. 3A.

[0055]FIGS. 3A-3C depict a slice selection with a 3-channel system. FIG.
3A depicts RF waveforms for each of the three channels. Each waveform is
scaled by 1/3 compared to the single channel waveform of FIG. 1A. The
waveform for channel 2 lags the waveform for channel 1 by Δt. The
waveform for channel 3 leads the waveform for channel 1 by Δt. The
gradient waveform is unchanged from the single channel case of FIG. 1A.
FIG. 3B depicts transverse magnetization achieved by the 3-channel
system. This is essentially identical to that achieved by the single
channel system shown in FIG. 1B. FIG. 3C depicts SAR from transverse
component of B1 for the 3-channel system. Unlike the single channel
system, SAR for the three channel system is a function of location in the
z direction. Units are arbitrary, but are the same as in FIG. 1C for
comparison. Total SAR over the field of view is 1/3 that of the SAR for
the single channel system.

[0056]The achieved transverse magnetization Mxy resulting from the
3-channel excitation scheme is shown in FIG. 3B. The excited slice
profile is nearly identical to that achieved by a conventional single
channel excitation shown in FIG. 1B. FIG. 3C shows the SAR due to the
component of B1 in the x-y plane. Unlike SAR with a conventional
one-channel slice selective excitation, SAR in the 3-channel system has a
spatial variation. Units in FIG. 3C are arbitrary, but are the same as in
FIG. 1C for accurate comparison. SAR for the 3-channel system is equal to
or lower than SAR for the two-channel system at every point in the
imaging field of view (FOV). SAR averaged over the entire FOV is
decreased in the 3-channel excitation by a factor of 3.

[0058]FIGS. 5A-5C depict a reduced SAR slice selection for a thick slice
with a width one-half the field of view, with a 3-channel system. FIG. 5A
depicts RF and gradient waveforms. The time offset Δt is calculated
according to Equation (1.1) and is greater than for the thin slice
selection of FIG. 3. FIG. 5B depicts achieved transverse magnetization,
which is essentially the same as for the single channel system of FIGS.
4A-4C. FIG. 5c depicts relative SAR arising from the transverse component
of B1. Units are arbitrary, but are the same as for FIGS. 4A-4C to allow
comparison. SAR integrated over the FOV is 1/3 that of the single
transmitter system.

[0059]RF waveforms and excitation results for conventional single-channel
excitation and the 3-coil system are presented in FIGS. 4A-4C and 5A-5C
for a slice thickness equal to one half the imaging field of view. Such
excitation might be used for slab selective excitation for 3-dimensional
imaging. Although the shape of the SAR distribution across the imaging
FOV varies with slice thickness, the factor of transverse SAR reduction
is independent of slice thickness. For a given RF waveform, slice
thickness is increased by decreasing gradient amplitude. This results in
a longer delay time Δt, according to Equation (1.1), which is
illustrated in FIG. 5A.

[0060]This method can be extended to any number of RF channels, each
controlling current through a coil with linear phase distribution with a
different multiple of 2π phase variation across the imaging field of
view. Slice profiles nearly identical to the single-channel case are
obtained with transverse SAR reduction factor equal to the number of
channels.

[0061]FIG. 6 depicts a k-space representation of 3-channel excitation.
Each coil represents a point in excitation k-space. The distance Δk
between points represents the linear phase in the sensitivity profile of
each coil, in units of excitation k-space (i.e. cycles/cm). The dotted
line shows the trajectory through excitation k-space traversed by the z
gradient. The initial left-to-right path corresponds to the positive
gradient lobe. The subsequent right-to-left path corresponds to the
negative gradient refocusing lobe. The excitation from all three coils
traverse the same k-space trajectory in tandem.

[0062]Insight into this excitation scheme may be gained by considering the
excitation in k-space. As illustrated in FIG. 6, the three coils
correspond to three points in excitation k-space. When the gradient is
turned on and excitation begins, the excitation k-space is traversed. If
each coil is to produce an identical slice profile, the same excitation
k-space must be scanned by each coil. This is achieved by making the RF
waveforms the same but shifted in time relative to each other. The time
shift for each coil's RF waveform (relative to the constant phase coil,
coil number 1) depends on the speed of k-space traversal (i.e., gradient
strength) and on the separation of the three points in excitation k-space
(i.e., the amount of linear phase incorporated into each RF coil).

[0063]FIGS. 7A-7B depict a 3-channel excitation of an off-isocenter axial
slice. Movement of the slice profile off-isocenter is achieved by
modulating the RF waveforms by the appropriate frequency, as in
conventional slice selective excitation. For this example, this was
accomplished by adding the appropriate phase to each point of the RF time
envelope. FIG. 7A depicts transverse magnetization achieved by 3-channel
excitation of off-isocenter slice modulated 1/4 FOV to the left. FIG. 7B
depicts relative SAR due to transverse B1. The SAR profile shifts with
the slice. Total SAR across the imaging FOV is reduced by 1/3, which is
the same as for the unshifted case.

[0064]The slice selective transmit SENSE excitation can be modulated to an
off-isocenter slice location by modulation frequency offset of the RF
waveforms in the same manner used for off-isocenter selection of a
conventional slice selective excitation. Modulation off-isocenter causes
no change in the performance of the method and no change in SAR
reduction. The spatial SAR profile shifts along with the slice profile
when the center frequency of the RF waveform is changed. This is
illustrated in FIGS. 7A-7B.

[0065]FIGS. 8A-8C depict slice selective excitation with 8 RF channels.
FIG. 8A depicts RF waveforms 1 through 8 designed for coil sets having 0,
2π, -2π, 4π, -4π, 6π, -6π, and 8π linear phase
respectively. FIG. 8B depicts that the slice profile achieved is
essentially identical to that achieved by single channel system. FIG. 8c
depicts that the SAR for the 8-channel system integrated over the field
of view is 1/8 that of the single channel system.

[0066]The method can be extended to any number of channels, with decrease
in SAR by a factor of the number of channels. FIGS. 8A-8C shows results
for an eight-channel system, with coils varying from -6π phase through
8π linear phase over the imaging volume, for a slice thickness 1/16th
the field of view. In general, the degree of SAR decrease integrated over
the coil volume is proportional to the number of channels and is
unaffected by the slice thickness of the excitation. The shape of the SAR
distribution changes with slice thickness, as illustrated in FIGS. 3A-3C
and 4A-4C, and with the number of channels, as illustrated by FIGS. 3A-3C
and 8A-8C.

Performance for Off-Axial Slices

[0067]The above description is based on slice selection in a plane
perpendicular to the direction of phase variation of the RF coil
elements. For a twisted birdcage coil oriented along z, this corresponds
to excitation of an axial slice, i.e. in the x-y plane. If the desired
excitation is in a plane outside the true axial plane, the performance of
the method changes. The degree of SAR decrease remains unchanged, but the
slice flip angle profile becomes modulated by a sinusoidal function in
one in-slice direction. For a two coil system, this modulation has a
cosine form. For more coils, the modulation becomes a more complex
summation of sinusoids.

[0068]FIG. 9 depicts a 3-coil excitation of an off-axial slice visualized
in excitation k-space. As in the axial slice case, the three coils
represent three points in excitation k-space. Unlike the axial slice
case, the excitation k-space trajectories traversed by each coil for
off-axial slice excitation are not collinear.

[0069]Insight into the performance of the method for off-axial slices can
be gained by considering the coil configuration in excitation k-space.
This is illustrated for a 3-coil configuration in FIG. 9. For example,
illustrated is the case of 30° rotation of the slice toward the
plane of constant y. This is achieved by playing the gradient waveform
out over both the z and y gradient coils simultaneously, appropriately
weighted to give the correct rotated gradient direction and amplitude.
Although illustrated for a single off-axial plane, the following analysis
of the performance of the multiple coil slice selection method applies to
any off-axial plane.

[0070]The three coils correspond to three points in excitation k-space,
the same as in the axial slice case. In the axial slice case, the k-space
trajectory was only along the z axis, and all three coils deposited
excitation k-space energy along the z axis only, resulting in a one
dimensional excitation k-space and a resulting excitation which was
selective only in z, and constant in x and y. For the off-axial slice
case, the excitation becomes two dimensional, as the k-space trajectories
of the individual coils are no longer along the same line. The resulting
excitation will be selective in two dimensions (z and y in the particular
case illustrated in FIG. 9).

[0071]RF waveforms are designed for the off-axial slice case in the same
way as for the axial slice, but with a different time offset Δt
between the waveforms given now by

Δt=2nπ cos θ/γG (1.2)

where θ is the angle between the selected slice and the axial plane.
Equation (1.2) for the off-axial plane differs from Equation (1.1) for
the axial plane by the factor cos θ.

[0072]FIG. 10 depicts the performance of multiple coil excitation for
off-axial slices. Results are shown for a three-coil system, with RF
waveforms equally weighted. The top row of FIG. 10 shows a magnitude of
transverse magnetization as a function of location in z and y for various
values of θ, the angle of the slice plane with respect to the x-y
plane. Slice profile is graphed along three lines labeled 1, 2, and 3
representing the slice profile at isocenter (1), the slice profile 1/4
FOV away from isocenter (2), and along the in-slice direction (3). Slice
profile at isocenter remains unchanged at any off-axial angle θ.
Slice profile away from isocenter decreases in magnitude but retains the
same shape as at isocenter. Note that variation in slice profile
magnitude occurs in one in-slice direction (y in this case). There is no
variation in the other in-slice dimension (x in this case). Slice profile
remains nearly unchanged for off-axial angles up to 30°. SAR
reduction by 1/3 remains the same for any off-axial angle θ.

[0073]Simulation results are shown in FIG. 10 for the magnitude of the
transverse magnetization achieved by the 3-coil system for various values
of θ, i.e. slice planes with various angles from the axial plane.
For all of these values of θ, the transverse SAR reduction factor
of 3 is unchanged. However, for larger values of θ the modulation
of the magnitude of the slice profile in one in-plane direction
increases. The slice profile in the orthogonal in-slice direction remains
constant. For the results shown in FIG. 10, the RF waveforms are all of
the same magnitude.

[0074]In the example shown in FIG. 10, equal weighting of the three RF
waveforms gives a modulation of the slice profile as a function of
distance r from isocenter along one in-slice direction by a function

m(r)=1+2 cos(2πrΔk sin θ) (1.3)

[0075]where Δk is the distance between k-space points representing
each coil, as defined in FIG. 6.

[0076]Modulation of the slice profile magnitude occurs in one in-slice
direction, and the slice profile remains constant in the orthogonal
in-slice dimension. m(r) represents the Fourier transform of the
excitation k-space along a line orthogonal to the k-space path defined by
the constant slice select gradient. In particular, m(r) given in Equation
(1.3) represents the Fourier transform of the function

δ(k)+δ(k-Δk sin θ)+δ(k+Δk sin θ)
(1.4)

which reflects the equal weighting of the three RF waveforms. We denote
this weighting scheme as "1-1-1." Different weighting of the RF waveforms
will give different shape to m(r), which may be optimized for particular
imaging situations.

[0077]FIGS. 11A-11B depict the effect of nonuniform weighting of the RF
waveforms for a 3-channel system for a 30° off-axial slice. FIG.
11A depicts the magnitude of excitation profile in the in-slice direction
(equivalent to line 3 in FIG. 10) showing modulation of the excitation
amplitude. More uniform excitation is achieved with the 1-2-1 RF waveform
weighting scheme (coil 1 waveform has twice the amplitude of coils 2 and
3) than with the 1-1-1 scheme (all RF waveforms are equal in amplitude).
FIG. 11B depicts transverse SAR. Total SAR for the 1-2-1 scheme is 0.375
times the SAR of a single channel excitation, while total SAR for the
1-1-1 scheme is 0.333 times the single channel SAR. SAR reduction can be
traded off for improved homogeneity of slice profile for off axial slices
by adjusting the weighting of the RF waveforms, in this 3-channel example
or with any number of channels. Maximum SAR reduction occurs when RF
waveforms are equally weighted.

[0078]FIGS. 11A-11B show the results of excitation with the RF waveform of
coil 1 weighted with twice the magnitude of the RF waveforms of coils 2
and 3, with waveforms renormalized to still give 90° flip angle.
The corresponding k-space sampling function becomes

[0079]FIGS. 11A-11B show that the uniformity of slice profile magnitude is
improved with the 1-2-1 weighting, at the expense of slightly less SAR
reduction. SAR for the 1-1-1 weighting is 1/3 that of single channel
excitation, while SAR for the 1-2-1 scheme is 0.375 that of the single
channel excitation. This example shows that SAR reduction can be flexibly
traded off with slice profile uniformity for off-axial slices by
adjusting the relative weighting of the different coil RF waveforms. With
a large number of channels, the waveform design problem becomes a true
two-dimensional Fourier transform design problem, for which an arbitrary
in-plane slice profile can be prescribed. However, maximum SAR reduction
is achieved when the amplitude of the individual channel RF waveforms is
equal.

[0080]Described herein is a method of slice selection which utilizes
multiple transmit channels to achieve slice profiles identical to those
obtained by conventional single transmit channel slice selective pulses,
in the same excitation time, but with dramatic reduction of SAR by a
factor up to the number of transmit channels. The transverse component of
SAR is reduced by destructive interference of the RF excitation at
locations outside the selected slice.

[0081]This method is presented for hypothetical coil sensitivity profiles
which are constant in amplitude but with linearly varying phase. Such
coil sensitivity profiles may be possible with twisted birdcage coil
designs.

[0082]FIG. 12 depicts a system, for reducing a specific absorption rate
(SAR) over a field of view of an imaged object during magnetic imaging
(MRI), that includes a transmit module. In some embodiments, the transmit
module is programmed to emit a first radiofrequency (RF) pulse into an
object with an RF excitation coil element that has a first sensitivity
profile comprising a first phase that is substantially constant across an
imaging volume of the object; emit a second RF pulse into the object with
a second RF excitation coil element that has a second sensitivity profile
comprising a second phase that varies substantially linearly, with a
first nonzero integer multiple of 2π phase variation, in a direction
across the imaging volume; and emit a third RF pulse into the object with
a third RF excitation coil element that has a third sensitivity profile
comprising a third phase that varies substantially linearly, with a
second nonzero integer multiple of -2π phase variation, in the
direction across the imaging volume. In some embodiments, an improved
SAR, resulting from emission of the first, second, and third RF pulses
over a field of view of the object, is decreased relative to an
unimproved SAR, resulting from emission of a fourth RF pulse that would
produce substantially the same amount of transverse magnetization as
emission of the first, second, and third RF pulses over the field of
view.

[0083]Although preferred embodiments of the disclosure have been described
in detail, certain variations and modifications will be apparent to those
skilled in the art, including embodiments that do not provide all the
features and benefits described herein. It will be understood by those
skilled in the art that the present disclosure extends beyond the
specifically disclosed embodiments to other alternative or additional
embodiments and/or uses and obvious modifications and equivalents
thereof. In addition, while a number of variations have been shown and
described in varying detail, other modifications, which are within the
scope of the present disclosure, will be readily apparent to those of
skill in the art based upon this disclosure. It is also contemplated that
various combinations or subcombinations of the specific features and
aspects of the embodiments may be made and still fall within the scope of
the present disclosure. Accordingly, it should be understood that various
features and aspects of the disclosed embodiments can be combined with or
substituted for one another in order to form varying modes of the present
disclosure. Thus, it is intended that the scope of the present disclosure
herein disclosed should not be limited by the particular disclosed
embodiments described above.